Chapter 5 - Exponential and Logarithmic Functions - 5.3 One-to-One Functions; Inverse Functions - 5.3 Assess Your Understanding - Page 282: 99

(a) $60$, $(-6,60)$. (b) $-4$, $(-4,12)$. (c) $-2$.

(a) Given $H(x)=(\frac{1}{2})^x-4$, we have $H(-6)=(\frac{1}{2})^{-6}-4=60$ which gives a point $(-6,60)$. (b) For $H(x)=12$, we have $(\frac{1}{2})^x-4=12$ or $(\frac{1}{2})^x=16=(\frac{1}{2})^{-4}$, which gives $x=-4$ and a point $(-4,12)$. (c) Letting $H(x)=0$, we have $(\frac{1}{2})^x-4=0$ or $(\frac{1}{2})^x=4=(\frac{1}{2})^{-2}$, which gives $x=-2$.